MONTPELIER — House lawmakers gave preliminary approval Tuesday to legislation that would require every school district in the state to provide publicly funded preschool to children as young as 3.

In a 97-43 vote that split mostly along party lines, advocates for early education won a victory they say will expand opportunities for kids during a critical period in their lives. For lower-income children especially, supporters of the legislation say, the bill would provide the head start needed to promote academic success later in life.

“By investing in high-quality early education instruction, we create the foundation for learning that can’t be replicated later in life,” said Rep. Sarah Buxton, a Tunbridge Democrat. “Unfortunately, not all children have the early foundational supports that can help prevent lifelong difficulty with learning.”

Critics, however, said that however worthwhile preschool may be, lawmakers should not impose upon districts a new mandate for which local property tax payers will be picking up the tab.

Rep. Heidi Scheuermann, a Republican from Stowe, said it’s ironic that the House just last week voted out an education finance bill aimed at bending the spending trajectory in local schools.

“We were talking how we were going to control spending, and we were blaming ... local school boards for voting on budget increases and spending increases,” Scheuermann said.

Less than seven days later, she said, the same lawmakers are passing legislation that will necessarily increase local budgets.

“We can’t ask our residents to pay more,” Scheuermann said. “And yet the state is now forcing us to do that.”

Gov. Peter Shumlin seems to share at least some of the opponents’ concerns. The Democrat said he supports efforts to expand publicly financed preschool offerings. But he stopped short Tuesday of endorsing the House’s approach.

“There isn’t a Vermonter who doesn’t agree that pre-K is incredibly important. The question is how do we pay for it?” Shumlin said. “We’ve got to do it in a way that doesn’t adversely impact property tax payers, and that’s the balance we’re trying to find.”

Shumlin and lawmakers look to have at least another year to figure it out. With less than two weeks left in the session, the legislation approved by the House on Tuesday is exceedingly unlikely to get through the Senate before the fall of the gavel.

But proponents of the plan say the budgetary impacts won’t be nearly as pronounced as critics fear. All but 40 of the state’s 270 or so school districts already provide at least some publicly financed preschool; those programs now serve about 38 percent of the approximately 11,300 kids age 3 and 4.

Rep. Adam Greshin, a Warren independent, said that whether the Legislature acts or not, Vermont is already heading down the road to universal pre-kindergarten, as districts respond to demand from constituents. In fiscal year 2016, the first year the legislation would take effect, the Legislature’s Joint Fiscal Office predicts an annual fiscal impact of only $1.2 million.

Estimates from the Agency of Education project that pre-K enrollment percentages will plateau at 60 percent by 2020 and add $9.8 million annually to statewide school spending — a drop of water in the $1.4 billion public education bucket.

The legislation wouldn’t mandate enrollment in preschool, only that it be available to parents who want it; the bill calls for at least 10 hours of publicly funded preschooling for 35 weeks a year.

Rep. Johanna Leddy Donovan, a Burlington Democrat and chairwoman of the House Education Committee, said she’s convinced the additional expenditures will, in short order, result in downward pressure on budgets for special education.

Donovan said it’s also a matter of fairness. In districts without publicly funded preschool, she said, children from well-to-do families likely aren’t missing out on education. It’s the kids from low-income families, Donovan said, who are forced to go without.

Not everyone is convinced that the fiscal impacts of the mandate would be so benign, especially for towns in which parents opt in high numbers to avail themselves of the cost-free option.

Rep. Cynthia Browning, an Arlington Democrat, said that if lawmakers think preschool is important enough to mandate, then they ought to be willing to fund it as well.

Instead of leaving property tax payers to pay for the preschool-related expenses that will be built into their tax rates, Browning said the Legislature should allocate general fund revenues to offset what will otherwise become an unfunded mandate from Montpelier.

Rep. Margaret Cheney, a Democrat from Norwich, one of the districts that doesn’t offer publicly funded pre-K, said she agreed.

“I think the underlying issue here is not its value, but how we pay for it, and essentially whether we want to expand what the property tax pays for as opposed to the general fund,” Cheney said. “And I think that’s a very legitimate point, which I agree with.”

Rep. Chris Pearson, a Burlington Progressive, voted against the bill out of concern that it would undermine the public education apparatus that has adopted a growing role in delivering preschool services.

Under existing law, it’s left to schools to decide which pre-K programs they’ll fund. The legislation approved Tuesday would allow parents wider choice and permit them to enroll their children in “qualified” private settings outside the geographic boundaries of their home district.

Buxton, the Tunbridge representative, said more than 70 percent of children under 6 live in households in which all adults are working.

Improving enrollment rates in preschool, she said, will mean giving parents a range of options. She said the bill was carefully crafted to ensure that public dollars won’t be used to pay for placements at facilities that deliver religious instruction.

“By permitting a parent to enroll their child in a pre-K program that works for them … we expect that the enrollment in pre-K education will grow,” Buxton said.